All spectral dominant norms are stable

S. Friedland; C. Zenger

doi:10.1016/0024-3795(84)90206-4

All spectral dominant norms are stable

S. Friedland, C. Zenger

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Abstract

A vector norm |·|on the space of n×n complex valued matrices is called stable if for some constant K&>0, not depending upon A or m, we have |A^m|≤K|A|^m We show that such a norm is stable if and only if it dominates the spectralradius.

Original language	English
Pages (from-to)	97-107
Number of pages	11
Journal	Linear Algebra and Its Applications
Volume	58
Issue number	C
DOIs	https://doi.org/10.1016/0024-3795(84)90206-4
State	Published - Apr 1984

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title = "All spectral dominant norms are stable",

abstract = "A vector norm |·|on the space of n×n complex valued matrices is called stable if for some constant K&>0, not depending upon A or m, we have |Am|≤K|A|m We show that such a norm is stable if and only if it dominates the spectralradius.",

author = "S. Friedland and C. Zenger",

note = "Funding Information: *The first author was partially sponsored by the United States Army under Contract No. DAAG2WOCSS41 and by Binational Science Foundation under grant 3225.",

year = "1984",

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doi = "10.1016/0024-3795(84)90206-4",

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journal = "Linear Algebra and Its Applications",

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T1 - All spectral dominant norms are stable

AU - Friedland, S.

AU - Zenger, C.

N1 - Funding Information: *The first author was partially sponsored by the United States Army under Contract No. DAAG2WOCSS41 and by Binational Science Foundation under grant 3225.

PY - 1984/4

Y1 - 1984/4

N2 - A vector norm |·|on the space of n×n complex valued matrices is called stable if for some constant K&>0, not depending upon A or m, we have |Am|≤K|A|m We show that such a norm is stable if and only if it dominates the spectralradius.

AB - A vector norm |·|on the space of n×n complex valued matrices is called stable if for some constant K&>0, not depending upon A or m, we have |Am|≤K|A|m We show that such a norm is stable if and only if it dominates the spectralradius.

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U2 - 10.1016/0024-3795(84)90206-4

DO - 10.1016/0024-3795(84)90206-4

M3 - Article

AN - SCOPUS:0002620593

SN - 0024-3795

VL - 58

SP - 97

EP - 107

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - C

ER -

All spectral dominant norms are stable

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